Thiry samples of cheddar cheese were analyzed for their content of acetic acid, hydrogen sulfide and lactice acide. Each sample was tasted and scroed by a panel of judges and the average taste score produced. Used the cheddar data from faraway package to answer the following: a) Fit a regression model with taste as the response and the three chemical contents as predictors. Report the values of the regression coefficients b) Compute the correlation between the fitted values and the response. Square it. Identify where this value appears in the regression output c) Fit the same regression model but without the intercept term. What is the value of R reported in the output? Compute a more reasonable measure of the goodness-of-fit for this example d) Compute the regression coefficients from the original fit using the QR decomposition showing your R code